The keys (numbered $2$ to $9$) on a telephone keypad are associated with specific groups of lowercase English letters. Below is an example of how letters can be mapped to keys on a telephone keypad.

Note: The keys $1$, $*$, $0$, and $\#$ do not map to any letters.

In the above mapping, the key $2$ is mapped with letters ["a", "b", "c"]; pressing it once types "a", pressing it twice types "b", and pressing it three times types "c".

Any mapping is possible as long as each letter is assigned to exactly one key, and keys can be mapped to any number of distinct letters.

Given a string, word, consisting of lowercase English letters, return the minimum number of pushes needed to type it after remapping the keys.

Note: No mapping is provided in the input. You can devise any mapping if needed.

Constraints:

• $1 \leq$ word.length $\leq 10^3$

• word consists of only lowercase English letters.

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.